Percentage Difference

A Percentage Difference is a difference shown as a percentage.

Two Meanings!

"Percentage Difference" can have two meanings, but if you are comparing an old value to a new value people commonly use this method:

Comparing Old to New

Difference means to subtract one value from another.

For example the difference from 5 to 3 is: 5-3 = 2.

Percentage Difference means to show that difference as a percent of the old value ... so divide by the old value and make it a percentage:

So the percentage difference from 5 to 3 is: 2/5 = 0.4 = 40%

How to Calculate

Here are two ways to calculate a percentage difference, use whichever method you prefer:

Method 1

Step 1: Calculate the difference (subtract one value form the other)

Step 2: Divide that Difference by the old value (you will get a decimal number)

Step 3: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

Note: if the new value is greater then the old value, it is a percentage increase, otherwise it is a decrease.

Method 2

Step 1: Divide the New Value by the Old Value (you will get a decimal number)

Step 2: Convert that to a percentage (by multiplying by 100 and adding a "%" sign)

Step 3: Subtract 100% from that

Note: if the result is positive it is a percentage increase, if negative, just remove the minus sign and cal it a decrease.

Examples

Example: A pair of socks went from $5 to $6, what is the percentage difference?

Answer (Method 1):

Step 1: $5 to $6 is a $1 increase
Step 2: Divide by the old value: $1/$5 = 0.2
Step 3: Convert 0.2 to percentage: 0.2×100 = 20% rise.

Answer (Method 2):

Step 1: Divide new value by old value: $6/$5 = 1.2
Step 2: Convert to percentage: 1.2×100 = 120% (ie $6 is 120% of $5)
Step 3: Subtract 100%: 120% - 100% = 20%, and that means a 20% rise.

Another Example: There were 160 smarties in the box yesterday, but now there are 116, what is the percentage difference?

	Answer (Method 1): 160 to 116 is a decrease of 44. Compared to yesterday's value: 44/160 = 0.275 = 27.5% decrease.

	Answer (Method 2): Compare today's value with yesterday's value: 116/160 = 0.725 = 72.5%, so the new value is 72.5% of the old value. Subtract 100% and you get -27.5%, or a 27.5% decrease.

The Formula

You could also just put the values into this formula:

\|New Value - Old Value\|	× 100%

\|Old Value\|

(The "|" symbols mean absolute value, so negatives become positive)

Example: There were 200 customers yesterday, and 240 today:

\|240 - 200\|	× 100% = (40/200) × 100% = 20%

\|200\|

A 20% increase.

How to Reverse a Rise or Fall

Some people think that a percentage increase can be "reversed" by the same percentage decrease. But no!

For example, a 10% increase from 100 is an increase of 10, which equals 110 ...

... but a 10% reduction from 110 is a reduction of 11 (10% of 110 is 11), which equals 99 (not the 100 we started with)

Because the percentage rise or fall is in relation to the old value:

The 10% increase was applied to 100.
But the 10% decrease was applied to 110.

To "reverse" a percentage rise or fall, use the right formula here:

To Reverse:	Use this Percent:	Example 10%
An "x" percent rise:	x/(1+x/100)	10/(1+10/100) = 10/(1.1) = 9.0909...
An "x" percent fall:	x/(1-x/100)	10/(1-10/100) = 10/(0.9) = 11.111...

Or use this handy-dandy calculator (just type in a value and click in the other box)